**
DESCRIPTION: **
This course is an introduction to the mathematics of financial models.
The aim is to provide students with an introduction to some basic
models of finance and the associated mathematical machinery.

** OUTLINE: **
The course will begin with the development of the basic ideas of hedging and
pricing by arbitrage
in the discrete time setting of binomial tree models.
Key probabilistic concepts of conditional
expectation, martingale, change of measure, and representation,
will all be introduced first in this
simple framework as a bridge to the continuous model setting.
Mathematical fundamentals for the development and analysis of continous time
models will be covered, including Brownian motion, stochastic calculus, change
of measure, martingale representation theorem. These will then be combined
to develop the Black-Scholes option pricing formula.
Pricing and hedging for European and American call
options will be discussed.
Attention will then turn to models of the interest rate market.
Various models will be discussed, including the
Heath-Jarrow-Morton
and Cox-Ingersoll-Ross models.
As time permits, more general
models and extensions will be described.

** COMPUTER MODULES: **
These will complement the theoretical material presented in the course.
Students may wish to enrol in
Math 161 in the Fall of 1998, which will include an Introduction to Mathematica.

** TEXT: **

** REFERENCES: **

* Background in economics/finance:*

** MATHEMATICAL FINANCE TALKS AT UCSD **

Thursday, March 11, 1999, Price Center Theater, 5 p.m.

** LINKS TO RELATED WEB SITES (under construction):**

Please direct any questions to Professor Ruth J. Williams, email: williams@math.ucsd.edu